text: In Population-based rule evaluation, rules are applied to populations. All molecules of the same species in the same state are pooled together. Application of a specific rule reduces or increases the size of one of the pools, possibly at the expense of another.
  Some of the best-known classes of simulation approaches in computational biology belong to the population-based family, including  those based on the numerical integration of ordinary and partial differential equations and the Gillespie stochastic simulation algorithm.
  Differential equations describe changes in molecular concentrations over time in a deterministic manner. Simulations based on differential equations usually do not attempt to solve those equations analytically, but employ a suitable numerical solver.
  The stochastic Gillespie algorithm changes the composition of pools of molecules through a progression of randomness reaction events, the probability of which is computed from reaction rates and from the numbers of molecules, in accordance with the stochastic master equation.
  In population-based approaches, one can think of the system being modeled as being in a given state at any given time point, where a state is defined according to the nature and size of the populated pools of molecules. This means that the space of all possible states can become very large. With some simulation methods implementing numerical integration of ordinary and partial differential equations or the Gillespie stochastic algorithm, all possible pools of molecules and the reactions they undergo are defined at the start of the simulation, even if they are empty. Such "generate-first" methods scale poorly with increasing numbers of molecular states. For instance, it has recently been estimated that even for a simple model of CaMKII with just 6 states per subunits and 10 subunits, it would take 290 years to generate the entire reaction network on a 2.54 GHz Intel Xeon processor. In addition, the model generation step in generate-first methods does not necessarily terminate, for instance when the model includes assembly of proteins into complexes of arbitrarily large size, such as actin filaments. In these cases, a termination condition needs to be specified by the user.
  Even if a large reaction system can be successfully generated, its simulation using population-based rule evaluation can run into computational limits. In a recent study, a powerful computer was shown to be unable to simulate a protein with more than 8 phosphorylation sites ( phosphorylation states) using ordinary differential equations.
  Methods have been proposed to reduce the size of the state space. One is to consider only the states adjacent to the present state (i.e. the states that can be reached within the next iteration) at each time point. This eliminates the need for enumerating all possible states at the beginning. Instead, reactions are generated "on-the-fly" at each iteration. These methods are available both for stochastic and deterministic algorithms. These methods still rely on the definition of an (albeit reduced) reaction network - in contrast to the "network-free" methods discussed below.
  Even with "on-the-fly" network generation, networks generated for population-based rule evaluation can become quite large, and thus difficult - if not impossible - to handle computationally. An alternative approach is provided by particle-based rule evaluation.